Linear and nonlinear thermoelectric transport in a magnetic topological insulator nanoribbon with a domain wall

We theoretically investigate the thermoelectric transport in the nanoribbon of the magnetic topological insulator with a domain wall in the linear and nonlinear regimes. The Lorenz number $L$, the Seebeck coefficients ${S}_{c}$, and the thermoelectrical figure of merit $ZT$ in the linear response regime are obtained by the nonequilibrium Green's function method. These thermoelectric coefficients strongly depend on the configuration of the domain wall, that is, the configuration of the domain wall can regulate the thermoelectric transport performance. We also discuss the effect of the width of nanoribbon and the thickness of the domain wall on the thermoelectric coefficient. The results show that the N\'eel-type wall is more dependent on the size effect of the domain wall than the Bloch-type wall. For a device with a given width, we can always allow the setup to be in high performance thermoelectric transport by adjusting the configuration of the domain wall. Moreover, considering the disorder, the transmission coefficient is robust against disorder even if the disorder strength is very strong, and ${S}_{c}$ and $ZT$ are robust against moderate disorder. Finally, for a nonlinear situation, we calculate the maximum power-generation efficiency $\ensuremath{\eta}$ and the equivalent thermoelectric figure of merit $Z{T}_{M}$, indicating the potential application as an effective thermoelectric device.